Subroutine MIXDLYR

Function:

Compute the Mixed layer entrainment rate and/or Monin-Obukhov depth. ACCUMQ is the accumulator for buoyancy fluxes.

MIXDLYR returns an entrainment rate and a Monin-Obukhov depth These are used by VVELOC in RUN.

If the layer is entraining normally, it returns a K-T mixed layer. If the layer is detraining, return the entrainment rate needed to get the layer to the Monin-Obukhov depth in dt seconds. If the layer is unstable with the layer beneath, return the rate needed to deepen to 1000 meters in dt seconds

Parameters that control mixing:

The routine follows the Niiler-Kraus algorithm, with the coefficients passed through an object T_Mixed_Layer. The mixed layer may be sub-divided into several sub-layers so that the real "depth" of the mixed layer is equal to the sum of the layer thicknesses. The parameter which sets this is ml%nLayers.

ml%Sheareff:

The production of turbulence by release of shear energy at the base of the mixed layer is given by

H/2 * (%DELTA v)^2 * ml%sheareff

sheareff should therefore be between 0 and 1 larger values provide deeper mixed layers, especially near the equator.

ml%U3coeff:

The generation of turbulence by the wind is given by

TKEgen(HERE) = ml%u3coeff * forcing%U3(HERE)

where U3 is the cube of the friction velocity speed. Typical values are in the range of 1.25, but this will depend on the type of wind that is used: how high a time resolution is included, whether a climatology is used, etc. The biggest problem here is providing a good estimate of U*^3 in the first place. Remember that it is independent of direction, so watch out particularly when using vector averaged estimates of the stress to compute U*

ml%Dissipat:

A background dissipation of tukrbulent energy is presumed. The work done by the wind and shear that is available for deepening is reduced by the amount

H * ml%DISSIPAT

Increasing DISSIPAT will shallow all mixed layers

ml%Penfrac and ml%Pendepth:

The model includes the potential energy generation by penetrating radiation, by assuming a double exponential decay of short- wave energy flux. A large fraction of the energy is absorbed within a very short e-folding distance of the surface, and so its contribution to the potential energy is nil. The remaining part is assumed to decay over a length scale ml%Pendepth. The fraction of penetrating energy which decays on the longer length scale is given by ml%Penfrac. Larger values of Pendepth lead to deeper mixed layers because it provides heating at depth. Entrainment represents an increase in potential energy. This increase comes from the turbulence energy released through wind and shear. But if heating occurs at depth, not so much wind work is needed to get to the same change in potential energy. If the model is to be made interactive with biology, it may well become necessary to make penfrac and pendepth prognostic 2-dimensional arrays.

ml%QnegDiss:

When the surface heat flux is into the ocean, the turbulence must mix that new heat downward, even if a mixed layer already exists. A certain amount of potential energy must be generated to stir this additional heat down. The Monin-Obukhov theory says that if the heating is strong enough and the wind weak enough, that all of the mixed layer behavior can be described by this balance. (This happens when the new depth computed by the Monin-Obukhov theory is shallower than the pre-existing depth). When the surface heat flux is out of the ocean, the cooling of the surface represents a potential energy SOURCE, that convecting water dropping through the existing layer releases turbulent energy. This looks like an additional source of mixing and can give rise to extra deepening. Niiler and Kraus propose that the amount of potential energy release by cooling might be dissipated somewhat before becoming completely realized. Therefore there is a parameter ml%QNEGDISS which says how much of a negative surface buoyancy flux can be used in the energy budget for deepening. Values should be between 0 and 1. Smaller values will allow deeper winter-time mixed layers and more vigorous autumnal deepening It should have little effect on spring-summer shallowing, except during sporadic cooling events.

ml%BackU2:

When a layer deepens, it must take quiescent water and stir it up. The turbulence energy budget must reflect the fact that some energy goes into generating turbulence in the layer between H and H + W*dt. For this we assume a background level of turbulence kinetic energy, and presume that the energy needed to spin this up is

dH * ml%BACKU2

Syntax:

call MIXDLYR(g, state, ml, forcing, dtmix)

INTENT(IN) :: g,state,dtmix

Subroutines Called: